zgeev(3)

NAME

ZGEEV - compute for an N-by-N complex nonsymmetric matrix

A, the eigenvalues and, optionally, the left and/or right eigen

vectors

SYNOPSIS

SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA,  W,  VL,  LDVL,
VR, LDVR, WORK, LWORK, RWORK, INFO )
    CHARACTER     JOBVL, JOBVR
    INTEGER       INFO, LDA, LDVL, LDVR, LWORK, N
    DOUBLE        PRECISION RWORK( * )
    COMPLEX*16     A( LDA, * ), VL( LDVL, * ), VR( LDVR, *
), W( * ), WORK( * )

PURPOSE

ZGEEV computes for an N-by-N complex nonsymmetric matrix

A, the eigenvalues and, optionally, the left and/or right eigen

vectors. The right eigenvector v(j) of A satisfies

A * v(j) = lambda(j) * v(j)

where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies

u(j)**H * A = lambda(j) * u(j)**H

where u(j)**H denotes the conjugate transpose of u(j).

The computed eigenvectors are normalized to have Euclidean

norm equal to 1 and largest component real.

ARGUMENTS

JOBVL (input) CHARACTER*1

= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.

JOBVR (input) CHARACTER*1

= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.

N (input) INTEGER

The order of the matrix A. N >= 0.

A (input/output) COMPLEX*16 array, dimension (LDA,N)

On entry, the N-by-N matrix A. On exit, A has

been overwritten.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

W (output) COMPLEX*16 array, dimension (N)

W contains the computed eigenvalues.

VL (output) COMPLEX*16 array, dimension (LDVL,N)

If JOBVL = 'V', the left eigenvectors u(j) are

stored one after another in the columns of VL, in the same order

as their eigenvalues. If JOBVL = 'N', VL is not referenced.

u(j) = VL(:,j), the j-th column of VL.

LDVL (input) INTEGER

The leading dimension of the array VL. LDVL >= 1;

if JOBVL = 'V', LDVL >= N.

VR (output) COMPLEX*16 array, dimension (LDVR,N)

If JOBVR = 'V', the right eigenvectors v(j) are

stored one after another in the columns of VR, in the same order

as their eigenvalues. If JOBVR = 'N', VR is not referenced.

v(j) = VR(:,j), the j-th column of VR.

LDVR (input) INTEGER

The leading dimension of the array VR. LDVR >= 1;

if JOBVR = 'V', LDVR >= N.

WORK (workspace/output) COMPLEX*16 array, dimension

(LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >=

max(1,2*N). For good performance, LWORK must generally be larg

er.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

RWORK (workspace) DOUBLE PRECISION array, dimension

(2*N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value.
> 0: if INFO = i, the QR algorithm failed to com

pute all the eigenvalues, and no eigenvectors have been computed;

elements and i+1:N of W contain eigenvalues which have converged.

LAPACK version 3.0 15 June 2000

ZGEEV(3)